Institute of Automatic Control and Robotics, Warsaw University of Technology, 02-525 Warsaw, Poland.
Sensors (Basel). 2022 Aug 19;22(16):6221. doi: 10.3390/s22166221.
Hexagonal grids have many advantages over square grids and could be successfully used in mobile robotics as a map representation. However, there is a lack of an essential algorithm, namely, SLAM (simultaneous localization and mapping), that would generate a map directly on the hexagonal grid. In this paper, this issue is addressed. The solution is based on scan matching and solving the least-square problem with the Gauss-Newton formula, but it is modified with the Lagrange multiplier theorem. This is necessary to fulfill the constraints given by the manifold. The algorithm was tested in the synthetic environment and on a real robot and is entirely fully suitable for the presented task. It generates a very accurate map and generally has even better precision than the similar approach implemented on the square lattice.
六边形网格比正方形网格具有许多优势，可以成功地用于移动机器人作为地图表示。然而，目前缺少一个重要的算法，即 SLAM（同时定位和地图绘制），该算法可以直接在六边形网格上生成地图。本文解决了这个问题。该解决方案基于扫描匹配，并使用 Gauss-Newton 公式解决最小二乘问题，但通过拉格朗日乘子定理进行了修改。这是为了满足流形给出的约束。该算法已在合成环境和真实机器人上进行了测试，完全适用于所提出的任务。它生成了非常精确的地图，通常比在正方形晶格上实现的类似方法具有更高的精度。
